lol, oh no that'd take some pretty complicated plumbing.
I was thinking more along the lines of the barrel acting as a sump or water resivor for a central filtration system ... water passing into the barrel would receive some heat from the sun, before it drained back into the inside system ...
straight low tech and unregulated, other than by the laws of physics and thermodynamics. one could actually calculate the min and max temperatures the water in the system would acheive - and the more water in the system, the smaller the gap between min and max would be, as long as the pumps were operating.
the pump itself would also be contributing energy to the system, so you'd have figure that in as well as energy lost from evaporation.